# What is the vertex form of y=3x^2 +10x - 8 ?

Dec 29, 2017

$y = 3 {\left(x + \frac{5}{3}\right)}^{2} - \frac{49}{3}$

#### Explanation:

$\text{the equation of a parabola in "color(blue)"vertex form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where "(h,k)" are the coordinates of the vertex and a}$
$\text{is a multiplier}$

$\text{to obtain this form use the method of "color(blue)"completing the square}$

• " the coefficient of the "x^2" term must be 1"

$\Rightarrow y = 3 \left({x}^{2} + \frac{10}{3} x\right) - 8$

• " add/subtract "(1/2"coefficient of x-term")^2" to"
${x}^{2} + \frac{10}{3} x$

$\Rightarrow y = 3 \left({x}^{2} + 2 \left(\frac{5}{3}\right) x \textcolor{red}{+ \frac{25}{9}} \textcolor{red}{- \frac{25}{9}}\right) - 8$

$\textcolor{w h i t e}{\Rightarrow y} = 3 {\left(x + \frac{5}{3}\right)}^{2} - \frac{75}{9} - 8$

$\Rightarrow y = 3 {\left(x + \frac{5}{3}\right)}^{2} - \frac{49}{3} \leftarrow \textcolor{red}{\text{in vertex form}}$